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WAEC 2018 - FURTHER MATHS ANSWERS

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WAEC 2018 - FURTHERMATHS ANSWERS

Monday, 9th April, 2018
Further Mathematics/Mathematics (Elective) 2 (Essay) 2hrs 30mins 09:30 a.m – 12:00 noon
Further Mathematics/Mathematics (Elective) 1 (Objective) 1hr 30mins 2:00p.m – 3:30 p.m
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Further Maths OBJ:
1-10: BCADDDDDBB
11-20: DBABCCDDCC
21-30: BCABBAABAB
31-40: CBADBDDCAB
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PLS NOTE THAT ^ MEANS RAISE TO POWER


(1)
X-3|2 2|+4|5 2 |+3|5 2|= -24
| -4 6-x| |2 6-x| |2 -4|

X-3(12-2x+8)+4(30-5x-4)+3(-20-4) = -24
X-3(20-2x)+4(26-5x)+3(-24)= -24
20x - 2x² - 60 + 6x + 104 - 20x - 72 = -24
-2x² + 6x - 60+104-72+24 = 0
-2x² + 6x - 4 = 0
Divide through by -2
X² - 3X + 2 = 0
X² - 2X - X + 2= 0
X(X-2)-1(X-2)=0
(X - 1)(X - 2)=0
X=1 OR X=2

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(2)
Log 3x - 3logx³+ 2 = 0
Log 3x - 3log3³/log3x + 2 = 0
Log3x - 3/log3x + 2 = 0
P - 3/p + 2 = 0 where P = log3x
P² - 3 + 2p = 0
P² + 2p - 3 = 0
(p + 3) ( p - 1) = 0
P = -3 OR p = 1
But log3x = p
when p = -3
Log3x = -3
X = 3-³ = 1/27
And when P = 1
Log3x = 1
X = 3¹ = 3
And X = 1/27 OR 3

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(3a) 
U= x-2 ; hence X = u+2
Therefore : 
X^3+5/(x-2)^4 = (u+2)^3+5/ (u+2-2)^4
=(u+2)^3+5/u^4

(3b) 
(u+2)^3+5/u^4 = (u+2)^3/u^4 + 5/u^4

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(4)
Sn = n/2[2a+(n-1)d]
S12 = 12/6[2a + 11d]
S12= 6[2a + 11d] = 168
2a + 11d = 28-------(1)
Also 
T3 = a + 2d = 7---------(2)
Multiplying 1 by 2
2a + 4d = 14
Eqn 1 minus Eqn 3 gives 
7d = 14
d = 2
Putting this in eqn 2
a + 2(2) = 7
a + (4) = 7
a = 7 - 4
a = 3
Common difference = 2
First term = 3

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(5)
TABULATE
cooking oil type|a|b|c|d|e|f|g|h
x|8|5|1|7|2|6|3|4
y|6|3|4|8|5|7|1|8
d|2|2|-3|-1|-3|-1|2|2
d²|4|4|9|1|9|1|4|4

£d² = 4+4+9+1+9+1+4+4 = 36

r = 1- 6£d²/n(n²-1)

= 1 - 6×36/8(8²-1)
= 1 - 216/504
= 1 - 0.43
= 0.57


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(6)
It follow that:
P(n) = 1/3 and p(k)¹ = 1 - 1/3 = 2/3
P(T) = 1/5 and P(T)¹ = 1- 1/5 = 4/5

Hence, 
probability that only one if the them will be solve the questions will be:

= (1/3 × 4/5) + (1/5 × 2/3)
= 4/15 + 2/15
= 6/15
= 2/5

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(7)
m = 3i - 2j ; n = 2i + 3j ; p = i + 6j

Therefore:
4(3i - 2j) +2(2i +3j) -3(-i + 6j)
12i - 8j + 4i + 6j + 3i - 18j
12i + 4i + 3i - 8j + 6j - 18j
19i = 20j

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(8)
m1 = 20kg
u1 = 8ms-1
m2 = 30kg
u2 = 50ms-1

(a)
In same direction 
m1u1 + m2u2 = (m1+m2)v
20 × 80 + 30 × 50 = (20+30)v
1600+1500 = 50v
3100/50 = 50/50
V = 62ms-1

(b)
In opposite direction
m1u1 - m2u2 = (m1 + u2)V
20×30 - 30×50 = (20+30)V
1600 - 1500 = 50V
100/50 = 50V/50
V = 2m/s

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(9)
Draw the pie chart diagram

radius is the same hence 
(y - 2)² + (X - 3)² = (y + 4)² + (X - 5)² = (y + 1)² + (X + 2)²
Taking the first pair 
Y² - 4y + 4 + x² - 6x + 9 = y² + 8y + 16 + x² - 10x + 25 
- 6x - 4y + 13 = -10x+8y+41
4x - 12y = 28
X = 3y = 7--------(1)

Taking the second pair 
Y² + 3y + 16+x² - 10x+25 = y²+ 2y + 1 + x²+ 4x + 4
-10x + 3y + 41 = 4x + 2y + 5
14x - 6y = 36
7x - 3y = 18---------(2)
Eqn 2 minus Eqn 1
6x = 11
X = 11/6
Put this into Eqn (1)
11/6 - 3y = 7
3y = 11/6 - 7
3y = 11 - 42/6
3y = -31/6
y = -31/18

(a) coordinates of centre is (11/6, -31/18)

(b) Radius r = √(y-2)²+(x-3)²
r = √-31/18 -2)² + 11/6 - 3)²
r= √13.85 + 1.36 
r = 3.9

(c) (X - 11/6)² + (y + 31/18)² = 3.9²
(X - 11/16)² + (y + 31/18)² = 15.21



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(15) 
(a)
DRAW THE DIAGRAM

(b)
(2.2) + 80(0.6) = 300(1.2) + 100 (3)
2.2B + 48 = 360 + 300
2.B + 48 = 660
2.2B = 660 - 48
2.2B = 612
Reation at B = 278.18N
Taking moment about B
80(2.1) + 300(1) = 2.2A + 100 (0.8)
224 + 300 = 2.3A + 80
524 - 80 = 2.2A
A = 444/2.2
Reaction a+ A = 201.82N




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